Grade 7 Math quiz

Grade 7 Math Quiz

Practice Grade 7 math questions about rational numbers, expressions, equations, percentages, proportional relationships, geometry, probability, and data. Use hints when needed, choose an answer, and review the explanation after each question.

1 Question 1 of 10
Not answered

Evaluate: -8 + 15 - 6

Hint: Work from left to right: first add -8 and 15, then subtract 6.
Explanation: -8 + 15 = 7. Then 7 - 6 = 1.
2 Question 2 of 10
Not answered

Simplify: 5x - 2x + 7

Hint: Combine only the like terms with x.
Explanation: 5x - 2x = 3x. The constant 7 stays the same, so the expression is 3x + 7.
3 Question 3 of 10
Not answered

Solve for x: 3x + 4 = 22

Hint: Subtract 4 from both sides, then divide by 3.
Explanation: Subtract 4 from both sides: 3x = 18. Divide by 3, so x = 6.
4 Question 4 of 10
Not answered

What is 30% of 150?

Hint: 10% of 150 is 15. Use that to find 30%.
Explanation: 10% of 150 is 15. Therefore 30% is 3 × 15 = 45.
5 Question 5 of 10
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A recipe uses 2 cups of flour for 5 cookies. How many cups of flour are needed for 20 cookies?

Hint: 20 cookies is 4 times as many as 5 cookies.
Explanation: Since 20 is 4 × 5, multiply the flour by 4: 2 × 4 = 8 cups.
6 Question 6 of 10
Not answered

Find the unit rate: 180 miles in 3 hours.

Hint: Divide the total miles by the number of hours.
Explanation: 180 ÷ 3 = 60. The unit rate is 60 miles per hour.
7 Question 7 of 10
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A triangle has angles 55° and 70°. What is the third angle?

Hint: The angles inside a triangle add up to 180°.
Explanation: 55° + 70° = 125°. Then 180° - 125° = 55°.
8 Question 8 of 10
Not answered

What is the area of a circle with radius 5? Use π = 3.14.

Hint: Use the formula A = πr².
Explanation: A = πr² = 3.14 × 5² = 3.14 × 25 = 78.5.
9 Question 9 of 10
Not answered

A bag contains 4 yellow, 6 black, and 5 white counters. What is the probability of choosing a black counter?

Hint: Probability = number of favorable outcomes divided by total outcomes.
Explanation: There are 6 black counters and 15 counters total. The probability is 6/15.
10 Question 10 of 10
Not answered

Find the median of the data set: 18, 12, 25, 20, 15, 30, 10.

Hint: Put the numbers in order first, then find the middle value.
Explanation: Order the data: 10, 12, 15, 18, 20, 25, 30. The middle value is 18.

Your result

You answered 0 out of 10 questions correctly.

Grade 7 map

Grade 7 math is where separate skills start behaving like one connected system

This quiz moves through rational numbers, expressions, equations, percent, proportional relationships, unit rates, triangle angles, circle area, probability, and median. Instead of treating those as ten unrelated topics, Grade 7 is a good point to start asking: what relationship is this problem testing?

IntegersExpressionsEquationsPercent ProportionsGeometryProbabilityData
Integer checkpoint

Signed numbers make direction part of the calculation

Quiz expression -8 + 15 - 6 = 1
-8071
Move from -8 to 7 by adding 15, then move 6 units left. The signs describe direction, not just decoration around the digits.
Proportion engine

The recipe problem and the unit-rate problem are two versions of the same proportional idea

Grade 7 proportional reasoning becomes much easier when you can move between a scale factor and a per-one-unit rate.

Scale factor: recipe

2 cups make 5 cookies. Going from 5 cookies to 20 cookies multiplies the amount by 4.

2 × 4 = 8 cups

Unit rate: travel

180 miles in 3 hours becomes a per-one-hour rate by dividing both quantities by 3.

180 ÷ 3 = 60 miles/hour
Same structure, different direction: scale up when the multiplier is obvious; reduce to one unit when you need a rate.
Expression

Simplify what is already written

There is no equals sign, so there is no unknown value to solve for.

5x - 2x + 7
Combine like terms: 5x - 2x = 3x
Keep the constant: +7
Result: 3x + 7
Equation

Undo operations to isolate x

An equation gives a balance condition. Every transformation must preserve that balance.

3x + 4 = 22
Subtract 4: 3x = 18
Divide by 3: x = 6
Check: 3(6) + 4 = 22
Geometry studio

Two geometry questions, two very different invariants

For a triangle, the fixed fact is the angle sum. For a circle, the relationship is built into the area formula.

Triangle angle sum

55° + 70° + ? = 180°
third angle = 55°

Circle area

A = πr² = 3.14 × 25 = 78.5
Median lens

Median is about position after sorting

The original order is irrelevant. Once sorted, the center value is visible.

10121518202530
Probability lens

Probability is favorable outcomes over the relevant total

There are 6 black counters out of 15 counters altogether.

6 favorable9 other
P(black) = 6/15 = 2/5
Grade 7 extension

Reverse the percent question instead of only finding “30% of 150”

A stronger version asks: 45 is 30% of what number? This turns a direct percentage calculation into an equation.

0.30x = 45
x = 45 ÷ 0.30
x = 150
After the quiz

Review by skill cluster, not just by total score

A score of 7/10 can mean very different things. The useful question is which kind of relationship caused the mistakes?

Number senseintegers, percent, rational values
Algebralike terms, equations, inverse operations
Proportionscale factors, recipes, unit rates
Geometry & dataangle sum, circle area, median, probability